I. Field of the Invention
This invention relates, in general, to computer program media, methods, and systems for engineering analysis purposes and, in particular, to computer program media, methods and systems for simulating the dynamic response of a complex structural-acoustic system over a broad range of frequencies and wavelengths.
II. Description of Related Art
The analysis of the response of a coupled structural-acoustic system to external excitation becomes increasingly difficult with increasing excitation frequency. The main reason for this lies in the fact that the wavelength of the system deformation reduces with increasing frequency, making it difficult to devise a precise mathematical model that can adequately capture the complex response pattern. Traditionally, finite element analysis (FEA) has been used as an analysis method for low frequency vibrations while statistical energy analysis (SEA) has been used to analyze high frequency vibrations.
FEA Las not been used to predict high frequency vibrations because it is generally considered that approximately eight elements must be used to adequately resolve each structural wavelength, leading to unfeasibly large models at higher frequencies. Another difficulty with FEA is that the system response becomes increasingly sensitive to geometrical imperfections as the wavelength of the response decreases, so that even a very detailed deterministic mathematical model based on the nominal system properties may not yield a reliable response prediction.
A totally different, more approximate technique, SEA, is used to simulate the dynamic response of complex structural-acoustic system at high frequencies. With SEA, a complex system is modeled as a collection of subsystems, each of which is assigned a single response variable corresponding to the vibrational energy. It is generally recognized that for successful application of SEA, in addition to other conditions, each subsystem must ideally contain a number of resonant modes over the analysis band of interest. One implication of this condition is that the wavelength of the subsystem deformation must be of the same order as, or less than, the dimensions of the subsystem. In some cases this requirement may be only partially met: for example, in-plane waves in a plate are generally of much longer wavelength than bending waves, so that while the bending motion might meet the SEA requirement, the in-plane motion might not. This problem of both short and long wavelength deformations within a structure is exacerbated with decreasing frequency, i.e., lower frequencies.
Consequently, an approach for estimating the dynamic response of a structural-acoustic system at low frequency ranges has not been successful for estimating the dynamic response at high frequency ranges and vice versa. A need therefore exists for a single system or approach that represents the dynamic response of a structural-acoustic system at low frequencies and high frequencies, i.e., a broad range of frequencies.
A recent approach to the vibration analysis of complex systems is fuzzy structure theory. In this approach, a system is modeled as a master structure with a set of uncertain or fuzzy attachments. For example, the master structure might represent a ship hull and the fuzzy attachments might be internal systems consisting of items such as piping and mechanical or electrical equipment. A key result of fuzzy structure theory is that the attached items act mainly to provide damping to the master structure and, furthermore, the level of this damping is surprisingly independent of the dissipation factor of the attachments.
However, fuzzy structure theory is unproved for vibration analysis of complex systems; it is only known to have been applied to relatively simple systems. Moreover, the method has not been widely adopted in the engineering community due to several deficiencies. Specifically, fuzzy structure theory does not handle the transfer of loads on a secondary structure as equivalent loads on a primary structure in a generic way, and does not provide a generally applicable means for recovering a quantitative estimate of secondary structure response. Additionally, the mathematical basis of fuzzy structure theory has not been sufficiently fundamental for it to be integrated in unambiguous way into both existing low frequency deterministic analyses--such as finite element analysis--or into high frequency statistical analysis--such as SEA.